# Variation of parameters - i have different particular soluti

omar yahia
i was trying to get a particular solution of a 3rd order ODE using the variation of parameters method
the homogeneous solution is yh = c1 e-x + c2 ex + c3 e2x
the particular solution is yp=y1u1+y2u2+y3u3
as u1=∫ (w1 g(x) /w) dx , u2=∫ (w2 g(x) /w) dx , u3=∫ (w3 g(x) /w) dx
w =
|y1 y2 y3|
|y'1 y'2 y'3|
|y''1 y''2 y''3|

when i choose y1 , y2 , y3 to be e-x,ex,e2x i get an answer ,
but when i change the arrangement (like: ex,e-x,e2x )
i get another different answer !

so , i have two questions
1 is it normal to have different results when changing who is y1 , y2 , y3 , or am i doing something wrong?
2 if it is normal , does that mean i can have too many different particular solutions , just by changing who is y1 , y2 , y3?

Mentor
What are the different answers you get?
Maybe they are equivalent, and just look differently?

omar yahia
What are the different answers you get?
Maybe they are equivalent, and just look differently?

ummmmmm ... ahhhh .. actually ... when you asked me to show the results i went to prepare them for uploading
and as i was rewriting the solution i discovered an extra (2) multiplied in one little tiny term , will i fixed it and went on , and the results were the same indeed , i am terribly sorry for this mistake it happened because i trusted the solution of a senior without a thorough revision